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Journal articles on the topic 'ENTANGLEMENT CRITERION'

Author: Grafiati

Published: 11 September 2023

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1

Chen, Xiao-Yu, Li-Zhen Jiang, and Zhu-An Xu. "Necessary and sufficient criterion for k-separability of N-qubit noisy GHZ states." International Journal of Quantum Information 16, no. 04 (June 2018): 1850037. http://dx.doi.org/10.1142/s0219749918500375.

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A Multipartite entangled state has many different kinds of entanglements specified by the number of partitions. The most essential example of multipartite entanglement is the entanglement of multi-qubit Greenberger–Horne–Zeilinger (GHZ) state in white noise. We explicitly construct the entanglement witnesses for these states with stabilizer generators of the GHZ states. For an [Formula: see text] qubit GHZ state in white noise, we demonstrate the necessary and sufficient criterion of separability when it is divided into [Formula: see text] parties with [Formula: see text] for arbitrary [Formula: see text] and [Formula: see text]. The criterion covers more than a half of all kinds of partial entanglements for [Formula: see text]-qubit GHZ states in white noise. For the rest of multipartite entanglement problems, we present a method to obtain the sufficient conditions of separability. As an application, we consider [Formula: see text] qubit GHZ state as a codeword of the degenerate quantum code passing through depolarizing channel. We find that the output state is neither genuinely entangled nor fully separable when the quantum channel capacity reduces from positive to zero.

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2

Wang, Hailong, and Yunpeng Shi. "Multi-Mode Correlation in a Concurrent Parametric Amplifier." Photonics 9, no. 7 (June 23, 2022): 443. http://dx.doi.org/10.3390/photonics9070443.

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A concurrent parametric amplifier consisting of two pump beams is used to investigate the possibility of generating multi-mode correlation and entanglement. The existence of three-mode entanglement is demonstrated by analyzing the violation degree of three-mode entanglement criteria, including the sufficient criterion, i.e., two-condition and optimal single-condition criterion, and necessary and sufficient criterion, i.e., positivity under partial transposition (PPT) criterion. Besides, two-mode entanglement generated from any pair is also studied by using the Duan criterion and PPT criterion. We find that three-mode entanglement and two-mode entanglement of the two pairs are present in the whole parameter region. Our results pave the way for the realization and application of multi-mode correlation and entanglement based on the concurrent parametric amplifiers.

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3

Cheng, Wei, Fang Xu, and Hua Li. "A class of bound entangled states violating the Breuer–Hall criterion." Modern Physics Letters B 28, no. 20 (August 10, 2014): 1450164. http://dx.doi.org/10.1142/s0217984914501644.

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A strong and computational entanglement criterion, i.e. the Breuer–Hall criterion, has been proposed independently by Breuer [Phys. Rev. Lett. 97 (2006) 080501; J. Phys. A: Math. Gen. 39 (2006) 11847] and Hall [J. Phys. A: Math. Gen. 39 (2006) 14119]. As the first explicit example, we show that the class of bound entangled states found by Fei et al. [Phys. Lett. A 352 (2006) 321] exactly violate the Breuer–Hall criterion. This example can be considered as one of the test platforms of a variety of entanglement criteria and may be helpful for us to develop more powerful entanglement criteria.

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4

Hua, Zhang, and Wu Xiao-Hua. "Entanglement Criterion of N -Qubit State." Communications in Theoretical Physics 45, no. 4 (April 2006): 601–4. http://dx.doi.org/10.1088/0253-6102/45/4/006.

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5

PING, YUN-XIA, BO ZHANG, ZE CHENG, and QINFENG XU. "TWO-MODE ENTANGLEMENT VIA SUPERPOSITIONS OF TWO-MODE COHERENT STATES." Modern Physics Letters B 21, no. 19 (August 20, 2007): 1253–59. http://dx.doi.org/10.1142/s0217984907013584.

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Two-mode entanglement of superposition states from several two-mode coherent states is investigated according to the entanglement criterion.9 The dependence of entanglement on relative phase angle, coherent amplitude of each mode and phase angle is discussed. It is shown that under certain conditions the superposition states can exhibit entanglement properties.

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6

Li, Jun, and Lin Chen. "Entanglement criterion via general symmetric informationally complete measurement." Journal of Physics A: Mathematical and Theoretical 55, no. 1 (December 6, 2021): 015302. http://dx.doi.org/10.1088/1751-8121/ac3859.

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Abstract We propose entanglement criteria for multipartite systems via symmetric informationally complete measurement and general symmetric informationally complete measurement. We apply these criteria to detect entanglement of multipartite states, such as the convex of Bell states, entangled states mixed with white noise. It is shown that these criteria are stronger than some existing ones.

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7

ZHANG, BO, GUO-QIN GE, and YUN-XIA PING. "ENTANGLEMENT FOR THE TWO-MODE FIELD IN THREE-LEVEL ATOMIC SYSTEMS." Modern Physics Letters B 21, no. 13 (May 30, 2007): 781–88. http://dx.doi.org/10.1142/s0217984907013249.

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We investigate entanglement for the two-mode field in three-level atomic systems. Entanglement of the system is demonstrated according to the Duan's criterion.16 It shows that the entanglement has a close relation with the pump intensity. For large pump intensity, particular choice of its phase, zero detuning and cooperativity parameter, perfect entanglement for the two-mode field can be generated outside the cavity.

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8

Inui, Yoshitaka, and Yoshihisa Yamamoto. "Entanglement and Photon Anti-Bunching in Coupled Non-Degenerate Parametric Oscillators." Entropy 23, no. 5 (May 17, 2021): 624. http://dx.doi.org/10.3390/e23050624.

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We analytically and numerically show that the Hillery-Zubairy’s entanglement criterion is satisfied both below and above the threshold of coupled non-degenerate optical parametric oscillators (NOPOs) with strong nonlinear gain saturation and dissipative linear coupling. We investigated two cases: for large pump mode dissipation, below-threshold entanglement is possible only when the parametric interaction has an enough detuning among the signal, idler, and pump photon modes. On the other hand, for a large dissipative coupling, below-threshold entanglement is possible even when there is no detuning in the parametric interaction. In both cases, a non-Gaussian state entanglement criterion is satisfied even at the threshold. Recent progress in nano-photonic devices might make it possible to experimentally demonstrate this phase transition in a coherent XY machine with quantum correlations.

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9

Sarbicki, Gniewomir, Giovanni Scala, and Dariusz Chruściński. "Enhanced realignment criterion vs linear entanglement witnesses." Journal of Physics A: Mathematical and Theoretical 53, no. 45 (October 28, 2020): 455302. http://dx.doi.org/10.1088/1751-8121/abba46.

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10

Nian-Quan, Jiang, and Wangyu-Jian. "Criterion for Genuine Multipartite Entanglement Quantum Channels." Chinese Physics Letters 27, no. 1 (January 2010): 010302. http://dx.doi.org/10.1088/0256-307x/27/1/010302.

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11

Valdés-Hernández, A., L. de la Peña, and A. M. Cetto. "Strong entanglement criterion involving momentum weak values." Physics Letters A 383, no. 9 (February 2019): 838–42. http://dx.doi.org/10.1016/j.physleta.2018.11.053.

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12

JIANG, LI-ZHEN, XIAO-YU CHEN, TIAN-YU YE, FANG-YU HONG, and LIANG-NENG WU. "ENTANGLEMENT CRITERION FOR COHERENT SUBTRACTION AND COHERENT ADDITION OF BIPARTITE CONTINUOUS VARIABLE STATES." International Journal of Quantum Information 11, no. 06 (September 2013): 1350060. http://dx.doi.org/10.1142/s0219749913500603.

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We study the entanglement conditions of two quite general classes of two-mode non-Gaussian states. Using computable cross norm and realignment criterion, we obtain the sufficient conditions of entanglement for coherently added or subtracted two-mode squeezed thermal states, and the sufficient condition of entanglement for any photon number entangled state (PNES) evolving in a thermal noise and amplitude damping channel.

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13

Ben-Aryeh, Y., and A. Mann. "Separability and entanglement of n-qubit and a qubit and a qudit using Hilbert–Schmidt decompositions." International Journal of Quantum Information 14, no. 05 (August 2016): 1650030. http://dx.doi.org/10.1142/s0219749916500301.

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Hilbert–Schmidt (HS) decompositions are employed for analyzing systems of [Formula: see text]-qubit, and a qubit with a qudit. Negative eigenvalues, obtained by partial-transpose (PT) plus local unitary (PTU) transformations for one qubit from the whole system, are used for indicating entanglement/separability. A sufficient criterion for full separability of the [Formula: see text]-qubit and qubit–qudit systems is given. We use the singular value decomposition (SVD) for improving the criterion for full separability. General properties of entanglement and separability are analyzed for a system of a qubit and a qudit and [Formula: see text]-qubit systems, with emphasis on maximally disordered subsystems (MDS) (i.e. density matrices for which tracing over any subsystem gives the unit density matrix). A sufficient condition that [Formula: see text] (MDS) is not separable is that it has an eigenvalue larger than [Formula: see text] for a qubit and a qudit, and larger than [Formula: see text] for [Formula: see text]-qubit system. The PTU transformation does not change the eigenvalues of the [Formula: see text]-qubit MDS density matrices for odd [Formula: see text]. Thus, the Peres–Horodecki (PH) criterion does not give any information about entanglement of these density matrices. The PH criterion may be useful for indicating inseparability for even [Formula: see text]. The changes of the entanglement and separability properties of the GHZ state, the Braid entangled state and the [Formula: see text] state by mixing them with white noise are analyzed by the use of the present methods. The entanglement and separability properties of the GHZ-diagonal density matrices, composed of mixture of 8[Formula: see text]GHZ density matrices with probabilities [Formula: see text], is analyzed as function of these probabilities. In some cases, we show that the PH criterion is both sufficient and necessary.

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14

Gudder, Stan. "Quantum Entanglement: Spooky Action at a Distance." Quanta 9, no. 1 (June 16, 2020): 1–6. http://dx.doi.org/10.12743/quanta.v9i1.113.

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Quantum entanglement is an important resource in quantum information technologies. Here, we study and characterize in a precise mathematical language some of the weird and nonintuitive features of quantum entanglement. We begin by illustrating why entanglement implies action at a distance. We then introduce a simple criterion for determining when a pure quantum state is entangled. Finally, we present a measure for the amount of entanglement for a pure state.Quanta 2020; 9: 1–6.

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15

Aniello, Paolo, and Cosmo Lupo. "On the Relation Between Schmidt Coefficients and Entanglement." Open Systems & Information Dynamics 16, no. 02n03 (September 2009): 127–43. http://dx.doi.org/10.1142/s1230161209000104.

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We consider the Schmidt decomposition of a bipartite density operator induced by the Hilbert-Schmidt scalar product, and we study the relation between the Schmidt coefficients and entanglement. First, we define the Schmidt equivalence classes of bipartite states. Each class consists of all the density operators (in a given bipartite Hilbert space) sharing the same set of Schmidt coefficients. Next, we review the role played by the Schmidt coefficients with respect to the separability criterion known as the 'realignment' or 'computable cross norm' criterion; in particular, we highlight the fact that this criterion relies only on the Schmidt equivalence class of a state. Then, the relevance — with regard to the characterization of entanglement — of the 'symmetric polynomials' in the Schmidt coefficients and a new family of separability criteria that generalize the realignment criterion are discussed. Various interesting open problems are proposed.

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16

Zhao, Chao-Ying, Qi-Zhi Guo, and Wei-Han Tan. "A novel entanglement criterion of two-qubit system." International Journal of Modern Physics B 34, no. 05 (February 17, 2020): 2050022. http://dx.doi.org/10.1142/s0217979220500228.

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The “separability problem” in quantum information theory is a quite important and well-known hard problem. The low-dimensional system satisfies the PPT criterion. However, the high-dimensional system problem has been shown to be NP-hard problem. In general, it is very difficult to find the analytic solution of the density matrix for the high-dimensional system. Therefore, getting an analytic solution for two-qubit system is an interesting and useful problem. We propose a novel criterion for separability and entanglement-verification of two-qubit system. We expressed the density matrix by a sum of a principal density matrix and six separable density matrices. The necessary and sufficient conditions for the two-qubit system include that if the four involved coefficients [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and the principal density matrix [Formula: see text] are separable, then the two-qubit system is separable, otherwise the two-qubit system is entangled. Finally, our criterion results in a totally different conclusion compared to Horodecki’s criterion. We believe that the new criterion is more stringent than existing PPT methods.

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17

Zangi, S. M., Jian-Sheng Wu, and Cong-Feng Qiao. "Combo separability criteria and lower bound on concurrence." Journal of Physics A: Mathematical and Theoretical 55, no. 2 (December 20, 2021): 025302. http://dx.doi.org/10.1088/1751-8121/ac3c80.

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Abstract Detection and quantification of entanglement are extremely important in quantum information theory. We can extract information by using the spectrum or singular values of the density operator. The correlation matrix norm deals with the concept of quantum entanglement in a mathematically natural way. In this work, we use Ky Fan norm of the Bloch matrix to investigate the disentanglement of quantum states. Our separability criterion not only unifies some well-known criteria but also leads to a better lower bound on concurrence. We explain with an example how the entanglement of the given state is missed by existing criteria but can be detected by our criterion. The proposed lower bound on concurrence also has advantages over some investigated bounds.

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18

Wang, Hailong, Yajuan Zhang, Xiong Zhang, Jun Chen, Huaping Gong, and Chunliu Zhao. "The Effect of Quantum Noise on Multipartite Entanglement from a Cascaded Parametric Amplifier." Photonics 10, no. 3 (March 13, 2023): 307. http://dx.doi.org/10.3390/photonics10030307.

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The tripartite entanglement generated from a cascaded parametric amplifier is always present in the whole gain region in the ideal condition. However, in practical applications, the quantum entanglement is very fragile and easily deteriorated by quantum noise from interactions with external environments, e.g., the avoidable attenuation and amplification operations may lead to some degradation effects on the quantum entanglement. Therefore, in this work, bipartite entanglement for the three pairs and tripartite entanglement in this cascaded parametric amplifier under the circumstances of attenuation and amplification operations are analyzed by using positivity under partial transposition criterion. The results show that tripartite entanglement is robust to the deterioration effects from the attenuation and amplification operations rather than bipartite entanglement. Our results may find some practical applications of multipartite quantum entanglement in quantum secure communications.

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19

Masanes, L., and A. Winter. "A non-distillability criterion for secret correlations." Quantum Information and Computation 10, no. 1&2 (January 2010): 152–59. http://dx.doi.org/10.26421/qic10.1-2-11.

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Within entanglement theory there are criteria which certify that some quantum states cannot be distilled into pure entanglement. An example is the positive partial transposition criterion. Here we present, for the first time, the analogous thing for secret correlations. We introduce a computable criterion which certifies that a probability distribution between two honest parties and an eavesdropper cannot be (asymptotically) distilled into a secret key. The existence of non-distillable correlations with positive secrecy cost, also known as bound information, is an open question. This criterion may be the key for finding bound information. However, if it turns out that this criterion does not detect bound information, then, a very interesting consequence follows: any distribution with positive secrecy cost can increase the secrecy content of another distribution. In other words, all correlations with positive secrecy cost constitute a useful resource.

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20

BATLE, J., M. CASAS, A. R. PLASTINO, and A. PLASTINO. "QUANTUM ENTROPIES AND ENTANGLEMENT." International Journal of Quantum Information 03, no. 01 (March 2005): 99–104. http://dx.doi.org/10.1142/s021974990500058x.

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The nature of quantum entropies, and its use in Quantum Information Theory in the form of (i) total entropy, (ii) relative entropy and (iii) conditional entropy is revisited. In this ordering, we first show the correlations existing between the total q-entropy and entanglement, quantified in the form of entanglement of formation. Then, we revisit the use of the quantum relative entropy as a measure of entanglement, and we finally discuss some features of the quantum conditional q-entropies, which are used in turn as a separability criterion.

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21

ACCARDI, LUIGI, TAKASHI MATSUOKA, and MASANORI OHYA. "ENTANGLED MARKOV CHAINS ARE INDEED ENTANGLED." Infinite Dimensional Analysis, Quantum Probability and Related Topics 09, no. 03 (September 2006): 379–90. http://dx.doi.org/10.1142/s0219025706002445.

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Entangled Markov chains (EMC) were so baptized on the basis of the conjecture that they provide examples of states, on infinite tensor products of matrix algebras, which are in some sense "entangled".2 In this paper we introduce the notion of multiple (or "many-body") entanglement and extend the two-body criterion of entanglement obtained in Ref. 17 to this case. We then apply this extension to EMC and prove that "generically" they satisfy the entanglement conditions.

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22

Zhao, Chao-Ying, Qi-Zhi Guo, and Wei-Han Tan. "A simple entanglement criterion of two-qubit system." International Journal of Modern Physics B 33, no. 18 (July 20, 2019): 1950197. http://dx.doi.org/10.1142/s0217979219501972.

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We present a novel method to judge the entanglement of two-qubit system, the density matrix of a two-qubit system can be constituted by the principle density matrix [Formula: see text] and the separable density matrices [Formula: see text]–[Formula: see text]. The necessary and sufficient conditions for the two-qubit system, the three involved coefficients p [Formula: see text] 0, p [Formula: see text] 0, p [Formula: see text] 0, and the principal density matrix [Formula: see text] being separable, then the two-qubit system is separable, otherwise the two-qubit system is entangled. Finally, the criterion for several known density matrices have been verified in this way.

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23

王, 银珠. "An Entanglement Criterion for States in N⊗+∞System." Advances in Applied Mathematics 03, no. 01 (2014): 17–21. http://dx.doi.org/10.12677/aam.2014.31003.

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24

Liu, Guangrong. "Quantum entanglement criterion based on extended complex plane." Journal of Physics: Conference Series 1634 (September 2020): 012167. http://dx.doi.org/10.1088/1742-6596/1634/1/012167.

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25

Chen, Xiao-yu. "Realignment entanglement criterion of phase damped Gaussian states." Quantum Information Processing 12, no. 12 (August 15, 2013): 3665–74. http://dx.doi.org/10.1007/s11128-013-0625-6.

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26

Shahrokhshahi, Reihaneh, and Olivier Pfister. "Large-scale multipartite entanglement in the quantum optical frequency comb." Quantum Information and Computation 12, no. 11&12 (November 2012): 953–69. http://dx.doi.org/10.26421/qic12.11-12-4.

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We show theoretically that multipartite entanglement is generated on a massive scale in the spectrum, or optical frequency comb, of a single optical parametric oscillator (OPO) emitting well above threshold. In this system, the quantum dynamics of the strongly depleted pump field are responsible for the onset of the entanglement by correlating the two-mode squeezed, bipartite-entangled pairs of OPO signal fields. (Such pairs are independent of one another in the undepleted, classical pump approximation.) We verify the multipartite nature of the entanglement by evaluating the van Loock-Furusawa criterion for a particular set of entanglement witnesses deduced from physical considerations.

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27

Chen, K., and L. A. Wu. "A matrix realignment method for recognizing entanglement." Quantum Information and Computation 3, no. 3 (May 2003): 193–202. http://dx.doi.org/10.26421/qic3.3-1.

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Motivated by the Kronecker product approximation technique, we have developed a very simple method to assess the inseparability of bipartite quantum systems, which is based on a realigned matrix constructed from the density matrix. For any separable state, the sum of the singular values of the matrix should be less than or equal to $1$. This condition provides a very simple, computable necessary criterion for separability, and shows powerful ability to identify most bound entangled states discussed in the literature. As a byproduct of the criterion, we give an estimate for the degree of entanglement of the quantum state.

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28

Arunachalam, Srinivasan, Nathaniel Johnston, and Vincent Russo. "Is absolute separability determined by the partial transpose?" Quantum Information and Computation 15, no. 7&8 (May 2015): 694–720. http://dx.doi.org/10.26421/qic15.7-8-10.

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The absolute separability problem asks for a characterization of the quantum states $\rho \in M_m\otimes M_n$ with the property that $U\rho U^\dagger$ is separable for all unitary matrices $U$. We investigate whether or not it is the case that $\rho$ is absolutely separable if and only if $U\rho U^\dagger$ has positive partial transpose for all unitary matrices $U$. In particular, we develop an easy-to-use method for showing that an entanglement witness or positive map is unable to detect entanglement in any such state, and we apply our method to many well-known separability criteria, including the range criterion, the realignment criterion, the Choi map and its generalizations, and the Breuer--Hall map. We also show that these two properties coincide for the family of isotropic states, and several eigenvalue results for entanglement witnesses are proved along the way that are of independent interest.

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29

Yu, C. S., H. S. Song, and Y. H. Wang. "Genuine tripartite entanglement semi-monotone for 2x2xn-dimensional systems." Quantum Information and Computation 7, no. 7 (September 2007): 584–93. http://dx.doi.org/10.26421/qic7.7-2.

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In this paper, we present a new approach to study genuine tripartite entanglement existing in $(2\times 2\times n)-$dimensional quantum pure states. By utilizing the approach, we introduce a particular quantity to measure genuine tripartite entanglement. The quantity is shown to be an entanglement monotone in 2-dimensional subsystems (semi-monotone) and reaches zero for separable states and $(2\times 2\times 2)-$dimensional $W$ states, hence is a good criterion to characterize genuine tripartite entanglement. Furthermore, the formulation for pure states can be conveniently extended to the case of mixed states by utilizing the kronecker product approximation technique. As applications, we give the analytic approximation for weakly mixed states, and study the genuine tripartite entanglement of two given weakly mixed states.

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30

CHENG, WEI, FANG XU, HUA LI, and GANG WANG. "ENTANGLEMENT OF CONVEX LINEAR COMBINATION AND CONSTRUCTION OF PPT ENTANGLED STATES." International Journal of Quantum Information 11, no. 01 (February 2013): 1350002. http://dx.doi.org/10.1142/s0219749913500020.

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Given two bipartite quantum states and the convex linear combination of them, we discuss the relation between the entanglement of the convex linear combination state and the entanglement of states being combined. This is achieved by characterizing quantum states quantitatively via the positive partial transpose (PPT) criterion and the computable cross-norm or realignment (CCNR) criterion. Inspired by the Horodecki's 3 ⊗ 3 quantum states, we also give explicit examples to illustrate all possible cases of convex linear combination. Finally, as an application of this method, we show how to construct new bipartite PPT entangled states from known PPT entangled states by convex linear combination.

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31

Ramos, R. V., and A. Karlsson. "Numerical analysis of entanglement properties of density matrices in C2ÄC2 systems." Quantum Information and Computation 2, no. 3 (April 2002): 222–39. http://dx.doi.org/10.26421/qic2.3-5.

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Quantum entanglement is an enigmatic and powerful property that has attracted much attention due to its usefulness in new ways of communications, like quantum teleportation and quantum key distribution. Much effort has been done to quantify entanglement. Indeed, there exist some well-established separability criterion and analytical formulas for the entanglement of bipartite systems. In both, the crucial element is the partial transpose of the density matrix. In this paper, we show numerically that one can also have information about the entanglement of bipartite state, in C2ÄC2, without looking at the partial transpose. We furthermore study properties of disentanglement operation, as well as properties of the relative entropy.

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32

Gharibian, S., H. Kampermann, and D. Bruss. "On global effects caused by locally noneffective unitary operations." Quantum Information and Computation 9, no. 11&12 (November 2009): 1013–29. http://dx.doi.org/10.26421/qic9.11-12-6.

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Given a bipartite quantum state $\rho$ with subsystems $A$ and $B$ of arbitrary dimensions, we study the entanglement detecting capabilities of locally noneffective, or cyclic, unitary operations [Fu, Europhys. Lett., vol. 75]. Local cyclic unitaries have the special property that they leave their target subsystem invariant. We investigate the distance between $\rho$ and the global state after local application of such unitaries as a possible indicator of entanglement. To this end, we derive and discuss closed formulae for the maximal such distance achievable for three cases of interest: (pseudo)pure quantum states, Werner states, and two-qubit states. What makes this criterion interesting, as we show here, is that it surprisingly displays behavior similar to recent anomalies observed for non-locality measures in higher dimensions, as well as demonstrates an equivalence to the CHSH inequality for certain classes of two-qubit states. Yet, despite these similarities, the criterion is not itself a non-locality measure. We also consider entanglement detection in bound entangled states.

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33

GOHM, ROLF. "KÜMMERER–MAASSEN-SCATTERING THEORY AND ENTANGLEMENT." Infinite Dimensional Analysis, Quantum Probability and Related Topics 07, no. 02 (June 2004): 271–79. http://dx.doi.org/10.1142/s0219025704001566.

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We give a new criterion for asymptotic completeness in Kümmerer–Maassen-scattering theory which is more directly in terms of the coupling. To this end we define the semigroup of dual extended transition operators. Asymptotic completeness holds if and only if this semigroup is ergodic. This may also be interpreted in terms of entanglement.

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34

Isar, Aurelian. "Entanglement Generation and Evolution in Open Quantum Systems." Open Systems & Information Dynamics 16, no. 02n03 (September 2009): 205–19. http://dx.doi.org/10.1142/s1230161209000153.

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In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we study the continuous variable entanglement for a system consisting of two independent harmonic oscillators interacting with a general environment. We solve the Kossakowski-Lindblad master equation for the time evolution of the considered system and describe the entanglement in terms of the covariance matrix for an arbitrary Gaussian input state. Using Peres–Simon necessary and sufficient criterion for separability of two-mode Gaussian states, we show that for certain values of diffusion and dissipation coefficients describing the environment, the state keeps for all times its initial type: separable or entangled. In other cases, entanglement generation, entanglement sudden death or a periodic collapse and revival of entanglement take place. We analyze also the time evolution of the logarithmic negativity, which characterizes the degree of entanglement of the quantum state.

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35

Jivulescu, Maria A., Nicolae Lupa, and Ion Nechita. "Thresholds for reduction-related entanglement criteria in quantum information theory." Quantum Information and Computation 15, no. 13&14 (October 2015): 1165–84. http://dx.doi.org/10.26421/qic15.13-14-5.

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We consider random bipartite quantum states obtained by tracing out one subsystem from a random, uniformly distributed, tripartite pure quantum state. We compute thresholds for the dimension of the system being traced out, so that the resulting bipartite quantum state satisfies the reduction criterion in different asymptotic regimes. We consider as well the basis-independent version of the reduction criterion (the absolute reduction criterion), computing thresholds for the corresponding eigenvalue sets. We do the same for other sets relevant in the study of absolute separability, using techniques from random matrix theory. Finally, we gather and compare the known values for the thresholds corresponding to different entanglement criteria, and conclude with a list of open questions.

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36

Androulakis, George, and Ryan McGaha. "Some Remarks on the Entanglement Number." Quanta 9, no. 1 (December 11, 2020): 22–36. http://dx.doi.org/10.12743/quanta.v9i1.140.

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Gudder, in a recent paper, defined a candidate entanglement measure which is called the entanglement number. The entanglement number is first defined on pure states and then it extends to mixed states by the convex roof construction. In Gudder's article it was left as an open problem to show that Optimal Pure State Ensembles (OPSE) exist for the convex roof extension of the entanglement number from pure to mixed states. We answer Gudder's question in the affirmative, and therefore we obtain that the entanglement number vanishes only on the separable states. More generally we show that OPSE exist for the convex roof extension of any function that is norm continuous on the pure states of a finite dimensional Hilbert space. Further we prove that the entanglement number is an LOCC monotone, (and thus an entanglement measure), by using a criterion that was developed by Vidal in 2000. We present a simplified proof of Vidal's result where moreover we use an interesting point of view of tree representations for LOCC communications. Lastly, we generalize Gudder's entanglement number by producing a monotonic family of entanglement measures which converge in a natural way to the entropy of entanglement.Quanta 2020; 9: 22–36.

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FEI, SHAO-MING, and XIANQING LI-JOST. "A NOTE ON QUANTUM ENTANGLEMENT AND PPT." International Journal of Quantum Information 07, no. 03 (April 2009): 587–93. http://dx.doi.org/10.1142/s0219749909005328.

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We study quantum states for which the PPT criterion is both sufficient and necessary for separability. We present a class of 3 × 3 bipartite mixed states and show that these states are separable if and only if they are PPT.

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Aschauer, H., J. Calsamiglia, M. Hein, and H. J. Briegel. "Local invariants for multi-partite entangled states allowing for a simple entanglement criterion." Quantum Information and Computation 4, no. 5 (September 2004): 383–95. http://dx.doi.org/10.26421/qic4.5-4.

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We present local invariants of multi-partite pure or mixed states, which can be easily calculated and have a straight-forward physical meaning. As an application, we derive a new entanglement criterion for arbitrary mixed states of $n$ parties. The new criterion is weaker than the partial transposition criterion but offers advantages for the study of multipartite systems. A straightforward generalization of these invariants allows for the construction of a complete set of observable polynomial invariants.

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Ferraro, E., A. Napoli, and A. Messina. "A criterion for entanglement in two two-level systems." Journal of Physics A: Mathematical and Theoretical 40, no. 43 (October 9, 2007): F935—F941. http://dx.doi.org/10.1088/1751-8113/40/43/f02.

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Guo, Yu, and JinChuan Hou. "Entanglement detection beyond the CCNR criterion for infinite-dimensions." Chinese Science Bulletin 58, no. 11 (April 2013): 1250–55. http://dx.doi.org/10.1007/s11434-013-5738-x.

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Chen, Xiao-Yu, and Li-Zhen Jiang. "What Criterion Can We Get From Precise Entanglement Witnesses?" IEEE Journal on Selected Areas in Communications 38, no. 3 (March 2020): 557–67. http://dx.doi.org/10.1109/jsac.2020.2969006.

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Zakharov, R. K., and E. K. Bashkirov. "ENTANGLEMENT IN NONLINEAR TWO-QUBIT TAVIS — CUMMINGS MODEL." Vestnik of Samara University. Natural Science Series 29, no. 2 (August 30, 2023): 72–80. http://dx.doi.org/10.18287/2541-7525-2023-29-2-72-80.

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In this work, we have studied the dynamics of entanglement of two identical superconducting qubits resonantly interacting with the one-mode field of a coplanar microwave cavity without loss through single-photon transitions in the presence of third- and fifth-order nonlinearities. Based on the solution of the equation of evolution of the system for the Fock initial states of the cavity field, the criterion of qubits entanglement negativity is calculated. The results of the negativity calculation show that for the initial separable states, the cavity nonlinearity can lead to a significant increase in the maximum degree of qubit entanglement. It is shown that for the initial entangledstates of qubits and intense cavity fields, taking into account nonlinearities leads to stabilization of the degree of entanglement of qubits in the cavity and contributes to the disappearance of the effect of the entanglement sudden death of qubits.

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Amazioug, M., and M. Nassik. "Control of atom-mirror entanglement versus Gaussian geometric discord with RWA." International Journal of Quantum Information 17, no. 05 (August 2019): 1950045. http://dx.doi.org/10.1142/s021974991950045x.

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In this study, we control the quantum correlations existing between a movable mirror and atoms in hybrid atom-optomechanical system using rotating wave approximation (RWA) in adiabatic regime. We use the Mancini criterion to measure the entanglement, the purity to quantify the degree of mixedness and the Gaussian geometric discord (GGD) to characterize the quantum correlations even beyond entanglement. We study the effect of the optomechanical cooling rate and the cooperativity atomic on the transfer of quantum correlations between the movable mirror and atoms under the thermal effect. We also investigate the robustness of the GGD with respect to entanglement by exploiting recent experimental parameters.

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Dat, Tran Quang, and Truong Minh Duc. "Higher-order nonclassical and entanglement properties in photon-added trio coherent state." Hue University Journal of Science: Natural Science 129, no. 1B (June 22, 2020): 49–55. http://dx.doi.org/10.26459/hueuni-jns.v129i1b.5685.

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This paper studies the higher-order nonclassical and entanglement properties in the photon-added trio coherent state (PATCS). We use the criterion of higher-order single-mode antibunching to evaluate the role of the photon addition operation. Furthermore, the general criteria for detection of higher-order three-mode sum squeezing and entanglement features in the PATCS are also investigated. The results show that the photon addition operation to a trio coherent state can enhance the degree of both the higher-order single-mode antibunching and the higher-order three-mode sum squeezing and enlarge the value of the higher-order three-mode entanglement factor in the photon-added trio coherent state. In addition, the manifestation of the single-mode antibunching and the entanglement properties are more obvious with increasing the higher values of orders.

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Giedke, G., J. Eisert, J. I. Cirac, and M. B. Plenio. "Entanglement transformations of pure Gaussian states." Quantum Information and Computation 3, no. 3 (May 2003): 211–33. http://dx.doi.org/10.26421/qic3.3-3.

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We present a theory of entanglement transformations of Gaussian pure states with local Gaussian operations and classical communication. This is the experimentally accessible set of operations that can be realized with optical elements such as beam splitters, phase shifts and squeezers, together with homodyne measurements. We provide a simple necessary and sufficient condition for the possibility to transform a pure bipartite Gaussian state into another one. We contrast our criterion with what is possible if general local operations are available.

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Tripathi, Vinay, Chandrashekar Radhakrishnan, and Tim Byrnes. "Covariance matrix entanglement criterion for an arbitrary set of operators." New Journal of Physics 22, no. 7 (July 28, 2020): 073055. http://dx.doi.org/10.1088/1367-2630/ab9ce7.

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Wasak, Tomasz, Piotr Szańkowski, Marek Trippenbach, and Jan Chwedeńczuk. "Cauchy–Schwarz inequality for general measurements as an entanglement criterion." Quantum Information Processing 15, no. 1 (November 13, 2015): 269–78. http://dx.doi.org/10.1007/s11128-015-1181-z.

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Andreev, V. A., V. I. Man'ko, O. V. Man'ko, and E. V. Shchukin. "Tomography of Spin States, the Entanglement Criterion, and Bell's Inequalities." Theoretical and Mathematical Physics 146, no. 1 (January 2006): 140–51. http://dx.doi.org/10.1007/s11232-006-0014-8.

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Huang, Xiaofen, Tinggui Zhang, Ming-Jing Zhao, and Naihuan Jing. "Separability Criteria Based on the Weyl Operators." Entropy 24, no. 8 (August 2, 2022): 1064. http://dx.doi.org/10.3390/e24081064.

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Entanglement as a vital resource for information processing can be described by special properties of the quantum state. Using the well-known Weyl basis we propose a new Bloch decomposition of the quantum state and study its separability problem. This decomposition enables us to find an alternative characterization of the separability based on the correlation matrix. We show that the criterion is effective in detecting entanglement for the isotropic states, Bell-diagonal states and some PPT entangled states. We also use the Weyl operators to construct an detecting operator for quantum teleportation.

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YU, Y. B., Z. T. SHI, H. T. WANG, Y. F. QIN, L. F. LAI, S. H. JIN, S. N. ZHU, et al. "THREE-COLOR CONTINUOUS-VARIABLE ENTANGLEMENT DIRECTLY PRODUCED IN AN OPTICAL SUPERLATTICE." International Journal of Quantum Information 07, no. 01 (February 2009): 427–34. http://dx.doi.org/10.1142/s0219749909004505.

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The three-color continuous-variable entanglement directly produced by a cascaded nonlinear process in an optical superlattice was investigated theoretically. This cascaded nonlinear process can be realized by using quasi-phase-matching technique in a quasiperiodic superlattice. In the first step, signal- and idle-beams can be generated by a parametric down-conversion. Then, the third beam can be obtained through sum-frequency of idle and pump. The degree of quadrature phase amplitude correlations between the three modes was discussed by a sufficient inseparability criterion with a single inequality for continuous-variable entanglement.

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